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Shelby Sell Sammie Meddaugh Emily Wojahn.  Transformation: Functions that map real number to real numbers.  Rigid Transformations: Leave the side.

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Presentation on theme: "Shelby Sell Sammie Meddaugh Emily Wojahn.  Transformation: Functions that map real number to real numbers.  Rigid Transformations: Leave the side."— Presentation transcript:

1 Shelby Sell Sammie Meddaugh Emily Wojahn

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3  Transformation: Functions that map real number to real numbers.  Rigid Transformations: Leave the side and shape of the graph unchanged (horizontal and vertical translations, reflections).  Non Rigid Transformations: Distort the shape of a graph (horizontal or vertical stretches and shapes).

4  If c is a positive real number: Horizontal y= f(x-c) A translation to the right by c units y= f(x+c) A translation to the right by c units Vertical y= f(x) + c A translation up by c units y= f(x) - c A translation down by c units

5 y= x y= abs(x – 2) 2 y= abs(x) y= x 2

6 Across the x-axis (x,y) (x,-y) y= -f(x) Across the y-axis (x,y) (-x,y) y= f(-x) Through the origin (x,y) (-x.-y) y= -f(-x)

7 Reflection over y axis Reflection over y= x axis Reflection over x axis

8 Horizontal Stretch/Shrink A stretch by a factor of c if c>1 A shrink by a factor of c if c<1 Vertical Stretch/Shrink A stretch by a factor of c if c> 1 A shrink by a factor of c if c<1 y= f (x/c) y= c f(x)

9 Graph of y = x² Multiply all red values by 3 to get coordinates for the new graph. Graph y = 3x² y = x² "Transformations on the Basic Parabola." W.A.E.C.E. Math Help. N.p., n.d. Web.

10 Graph of y = x² with a stretch of 3.

11  1.) Horizontal shift 2 units to the right y=(x-2) ²  2.) Stretch Vertically by factor 3 y=3(x-2) ²  3.) Vertical Translation 5 units up y=3(x-2) ² +5 Given y=x²

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15 Y= f(x) Entire functions absolute value  (change negative y values to positive) Y= - f(x) Only Negative y values

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17 A) y = ½x B) y = 3x C) y = 3(x + 2) 2 D) y = ½(x + 2) 2 2

18 A) y = ½(x - 3) 2 B) y = ½(x + 3) 2 C) y = 2(x - 3) 2 D) y = 2(x + 3) 2 3

19 A y = 0.5(x + 1) 4 B y = 0.5(x - 1) 4 C y = 2(x + 1) 4 D y = 2(x - 1) 4

20 Describe how the graph of y= x² can be transformed to the graph of the given equation A) Vertical translation up 3 units B) Horizontal translation to the right 3 units C) Horizontal translation to the left 3 units D) Vertical translation down 3 units Y=x²-3

21  Given function f, which of the following represents a vertical stretch by a factor of 3. C) y=f(9x/3) D)y=f(x)/3 A) y=f(3x) B) y=3f(x )

22  Given a function f, which of the following represents a vertical translation of 2 units upward, followed by a reflection across the y-axis.  A) y=f(-x) + 2C) y= -f(x-2)  B) y= 2-f(x)D) f(x) -2

23  TRUE OR FALSE?  The function y=f(x+3) represents a translation to the right by 3 units of the graph of y = f(x).

24  TRUE OR FALSE?  The function of y=f(x)-4 represents a translation down 4 units of the graph of y=f(x)

25  Write an equation whose graph is  Y=x ²; a vertical stretch by a factor of 3, then shift right 4 units  A) y=3(x-4) ²C) y=3x ² -4  B) y=-3x ² +4D) y=3(x+4) ²

26  Write an equation whose graph is  Y= x ; a shift left 2 units, then a vertical stretch y a factor of 2, and finally a shift down 4 units.  A) 2 x+2 -4C) 2 x-2 +4  B) 2(x+2) -4D) 3(x-2) +4

27  1.) B  2.) A  3.) A  4.) D  5.) B 6.) A 7.) False, it is translated left. 8.)True 9.) A 10.)A

28 transformations.html&qs=555_556_557_558_1191_2440_1192_2441_2442 Algebra%20II/Ready%20for%20web%20site/zTransformationMatchingGame.pdf Pre calculus- Eighth edition book "Transformations on the Basic Parabola." W.A.E.C.E. Math Help. N.p., n.d. Web.


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